In radio-frequency (RF) communications, multiple-input-multiple-output (MIMO) refers to using multiple antennas at both the transmitter and the receiver ends to enhance communication performance. The terms input and output in MIMO denote the radio channels that carry the input and output signals received by or transmitted from a communication device (e.g., a transceiver). MIMO, which is an important portion of modern wireless communication standards such as IEEE 802.11n (e.g., Wi-Fi), 4G, 3GPP Long Term Evolution (LTE), IEEE 802.16e (e.g., WiMAX), and others, can use transmit beamforming to significantly increase data throughput and link range without the need for additional bandwidth or increased transmission power. Practically, the majority of wireless communication standards including 802.11ac have adopted a multicarrier modulation scheme known as orthogonal frequency division multiplexing (OFDM), which is based on frequency division multiplexing (FDD) concept.
In OFDM, each data stream, instead of being modulated on a single wide-band carrier, is modulated on a large number (e.g., hundreds or even thousands) of parallel narrow-band adjacent sub-carriers (e.g., tones). For example, a serial data stream can be split into multiple slower data stream, and each stream can be modulated using a modulation scheme, such as quadrature amplitude modulation (QAM), or any other modulation scheme. The modulated subcarriers are then passed through an inverse fast Fourier transform (IFFT) module such as inverse discrete Fourier transform (IDFT) module that converts them into a single stream of analog data. In technologies based on 802.11ac standard, transmit (TX) beamforming is implemented via a spatial mapping matrix (e.g., Q). Currently, for single-stream TX beamforming, the maximum-ratio transmission (MRT) scheme is used, which requires that the transmitter have an accurate estimate of the per-subcarrier, per-TX antenna channel, amplitude and phase. Therefore, an inaccuracy in the channel estimate can potentially result in a partial or full loss of gains from the MRT.